Theorem bj-vtoclg1fv

Description: Version of bj-vtoclg1f with a disjoint variable condition on x , V . This removes dependency on df-sb and df-clab . Prefer its use over bj-vtoclg1f when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 14-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-vtoclg1fv.nf	$$⊢Ⅎx\psi$$
	bj-vtoclg1fv.maj	$$⊢x=A\to \left(\phi \to \psi \right)$$
	bj-vtoclg1fv.min	$$⊢\phi$$
Assertion	bj-vtoclg1fv	$$⊢A\in V\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-vtoclg1fv.nf	$$⊢Ⅎx\psi$$
2		bj-vtoclg1fv.maj	$$⊢x=A\to \left(\phi \to \psi \right)$$
3		bj-vtoclg1fv.min	$$⊢\phi$$
4		elissetv	$$⊢A\in V\to \exists xx=A$$
5	1 2 3	bj-exlimmpi	$$⊢\exists xx=A\to \psi$$
6	4 5	syl	$$⊢A\in V\to \psi$$